A six-dimensional hyperchaotic system selection and its application in DS-CDMA system

In this paper, we analyze the hyperchaotic properties of cellular neural network (CNN) systems based on Lyapunov exponents. A four-step algorithm for selecting the hyperchaotic system is proposed. Firstly, calculate the maximum absolute value of time sequences, which is one of the properties of chaotic system, noted as boundedness. Secondly, check another property of chaotic system: sensitive dependence on the initial conditions. Several systems can be identified as non-chaotic systems through above two steps, which saves lots of time to calculate the Lyapunov exponents. Then, calculate the Lyapunov exponents. If the largest Lyapunov exponent is negative, the system is identified as non-chaotic system. Finally, determine the given system is chaotic or not by the strange attractors and the time sequences. The binary hyperchaotic spread spectrum sequences can be generated by a six-dimensional CNN system. Some of the binary hyperchaotic sequences can be used in a direct sequence code division multiple access (DS-CDMA) system after selecting through a special rule. Simulation results prove the effectiveness of the six-dimensional CNN hyperchaotic sequences, compared with the m-sequence and second-order Chebyshev polynomial function.